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binary search in sorted arrays: a comprehensive tutorial with code examples

binary search is a highly efficient search algorithm used to find the position of a target value within a sorted array. its key advantage lies in its logarithmic time complexity (o(log n)), making it significantly faster than linear search (o(n)) for large datasets. this tutorial will provide a thorough understanding of binary search, covering its core concepts, implementation, advantages, limitations, and variations.

*1. core concepts and principles*

binary search works by repeatedly dividing the search interval in half. here's the breakdown of the steps:

*sorted array:* binary search requires the array to be sorted in ascending (or descending) order. the algorithm relies on this order to make informed decisions about where to search next.

*divide and conquer:* the algorithm follows the divide-and-conquer paradigm. it repeatedly divides the array into smaller sub-arrays until the target value is found or the sub-array becomes empty.

*midpoint comparison:* in each iteration, the algorithm finds the middle element of the current sub-array. it then compares this middle element with the target value.

*three possible outcomes:*
*target found:* if the middle element is equal to the target value, the search is successful, and the index of the middle element is returned.
*target is smaller:* if the target value is smaller than the middle element, the search continues in the left half of the sub-array (elements to the left of the middle element). this is because the target can only exist in the left half due to the sorted nature of the array.
*target is larger:* if the target value is larger than the middle element, the search continues in the right half of the sub-array (elements to the right of the middle element). this is because the target can only exist in the right half.

*termination:* the search terminates when either:
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